Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Exercise Set - Page 348: 103

Answer

$2x^{n+2}+4x^2$

Work Step by Step

Factor the numerators and the denominators, when needed to have: $\\=\dfrac{(x^n-2)(x^n+2)}{7x} \cdot \dfrac{7x(2x^2)}{x^n-2}$ Cancel the common factors to have: $\\\require{cancel}=\dfrac{\cancel{(x^n-2)}(x^n+2)}{\cancel{7x}} \cdot \dfrac{\cancel{7x}(2x^2)}{\cancel{x^n-2}} \\=(x^n+2)(2x^2) \\=2x^2(x^n)+2x^2(2) \\=2x^{n+2}+4x^2$
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